I think Facebook with 120 million members must be a contender with membership growing at a prodigious rate.

"We got more (members) in the last three months than in the first three years of our existence," Sandberg said November 2008

http://news.cnet.com/8301-17939_109-10081341-2.html

I know that wiki is not always that reliable, however, this link shows a table of membership of key sites.

http://en.wikipedia.org/wiki/List_of_social_networking_websites

Not being a fan of social websites I had absolutely no idea that Myspace was so big, however, in terms of monthly unique visitor numbers, comScore consider Facebook to be more popular.

According to comScore, MySpace was overtaken internationally by main competitor Facebook in April 2008, based on monthly unique visitors.

http://news.cnet.com/8301-13577_3-9973826-36.html

MySpace I think is the most popular by number of users. Then there is Facebook, Friendster, Hi5, Bebo, Orkut. Some are laregly popular in certain regions/countries but not in others so their user population is somewhat skewed. There are also more activity specific networking sites like Windows Live Spaces, Xanga, Flixter, Classmates.com, Linkedln which are more specific to blogging, movies, business etc.

It would seem that counting number of user accounts is a false metric - lots of them are generated automatically to generate spam.

In the UK, one organisation measures accesses to the sites - again, this could be skewed by automated accounts, but there are some recent stats here (UK only, though):
http://weblogs.hitwise.com/robin-goad/2008/12/facebook_youtube_christmas_social_...
1. Facebook (35.4%)
2. YouTube (19.3)
3. Bebo (9.7%)
4. MySpace (5.4%)
5. Yahoo! Answers (1.1%)
6. Club Peguin (0.7%)
7. Nasza Klasa (0.7%)
8. Windows Live Home (0.6%)
9. Tagged (0.6%)
10 BBC H2G2 (0.6%)

I would say Facebook, for my generation (I am 23) but my younger cousins use Bebo and I think people older than me tend to use Myspace. There is definately an age gap between the users of Bebo and facebook, although many people have both or all three. Facebook has the most members I think.